Topics in Applied Mathematics (5cr)

Evaluation scale

H-5

Content scheduling

PART1
1. Logic
2. Combinatorics
3. Permutations
4. Combinations
5. Divisibility
6. Euclidean algorithm
7. Congruence
8. Residue class ring
9. Hash functions and RSA
PART 2
10. Sequence
11. Sum
12. Series
13. Recursive equation
14. Graph theory

Objective

After completing the course the student can
- apply logical rules and notation
- compute and apply permutations and combinations
- apply the concepts and properties of divisibility and congruence
- process arithmetic and geometric sequences and sums
- calculate the sum of a converging infinite geometric series
- form Taylor polynomials and utilize them in numerical computation
- determine coefficients for Fourier-series expansions using mathematical computation tools

Content

- Fundamentals of logic
- Basics od number theory with applications
- Basics of combinatorics with applications
- Sequences and series
- Taylor series
- Fourier series

Materials

All course materials will be published in Itslearning.

Teaching methods

Part 1, Logic, combinatorics and number theory:
lectures, homework, self-study, exam

Part 2, •:
lectures, homework sessions, self-study, exam

Exam schedules

Assessment Schedule

Midterm Exam – Part 1: 28 October 2025
First Retake: 4 November 2025

Midterm Exam – Part 2: 16 December 2025
First Retake: (Date listed as 2025 — please verify and update if needed)

Final Retake Exam (for both parts): 13 January 2026
Exact times for all exams will be published in the official schedule.

Important:
Homework and exercises must be submitted by the specified deadlines. Late submissions will not be accepted, and there are no options to make up or retake missed tasks.

Student workload

Part 1:
Intro 1h
Lectures 9*2h
Exam 2h
Self-study (homework, preparing for exams etc.) ~46h.

Part 2:
Lectures 5*2h
Homework sessions 5*2h (Mandatory attendance)
Exam 2h
Self-study (homework, preparing for exams etc.) ~46h.

Evaluation methods and criteria

Achieve at least 50% of the points in both Midterm exams or retakes.
Submit at least 30% of the exercises is mandatory to pass the course.

Additional points from homework will improve your grade.

Failed (0)

Less than 50% of the points in one or both of the Midterm exams or retakes.
Unauthorized non-attendance exceeds 30% of homework sessions.

The student has not demonstrated sufficient achievement of the course learning objectives. They recognize and apply only a limited number of course concepts and lack the necessary skills to implement them effectively.

Additionally, the course will be failed if any instance of academic misconduct is detected. The first occurrence—whether misconduct or an attempt—will result in the rejection of the affected exam or assignment. A second offense will lead to failure of the entire course.

Assessment criteria, satisfactory (1-2)

Student has demonstrated having achieved the learning objectives of the course on satisfactory level. They recognize and can to some extent use most of the concepts of the course topics.

Assessment criteria, good (3-4)

Student has demonstrated having achieved the learning objectives of the course well.
They recognize and can use most of the concepts of the course topics, and are able to apply them on various study and work contexts.

Assessment criteria, excellent (5)

Student has demonstrated having achieved the learning objectives of the course on excellent level. They master the concepts of the course topics, and are able to fluently apply them on study and work contexts.

Qualifications

Previous mathematics courses of ICT engineering curriculum (or equivalent skills):
Introduction to Engineering Mathematics
Calculus

Further information

Itslearning and email